The importance of including triaxiality in a calculation of fission barrier
heights was indicated many times before [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
In particular, it was shown that the effect of both
quadrupole and a general hexadecapole nonaxiality, when accounted for
within the nonexact method of constrained minimization (used generally
in all selfconsistent studies), may reach 2.5 MeV
for some superheavy even-even nuclei, see Fig. 5 in [11]}.
Here, we extend our previous discussion of its role to
the odd and odd-odd nuclei and, at the same time, improve the treatment
by employing the exact IWF method in potentially most interesting cases.
